cp's OEIS Frontend

A324115 a(n) = A002487(A323244(n)).

%I A324115 #9 Feb 20 2019 21:43:01
%S A324115 0,1,1,1,1,1,1,2,0,3,1,3,1,1,1,2,1,2,1,4,-2,4,1,5,-1,7,1,5,1,3,1,4,3,
%T A324115 11,-1,3,1,1,-2,5,1,4,1,6,1,13,1,7,-2,7,1,7,1,3,-7,9,-2,25,1,8,1,76,1,
%U A324115 5,3,8,1,21,7,3,1,7,1,31,3,31,-3,13,1,10,-2,199,1,5,-4,101,-18,4,1,2,-12,43,11,266,-5,9,1,11,-1,4,1,6,1,13
%N A324115 a(n) = A002487(A323244(n)).
%C A324115 If there are no odd perfect numbers then A324201 gives the positions of all zeros after the initial a(1) = 0.
%H A324115 Antti Karttunen, <a href="/A324115/b324115.txt">Table of n, a(n) for n = 1..4473</a>
%F A324115 a(n) = A002487(A323244(n)), with the definition of A002487 extended to the negative arguments so that A002487(-n) = -A002487(n).
%F A324115 a(A324201(n)) = 0.
%o A324115 (PARI)
%o A324115 A002487(n) = if(abs(n)<=1, n, A002487(n\2) + if( n%2, A002487(n\2 + 1))); \\ This version works consistently also with negative arguments, so that a(-n) = -a(n). Except that it is very slow on large n.
%o A324115 A002487(n) = { my(s=sign(n), a=1, b=0); n = abs(n); while(n>0, if(bitand(n, 1), b+=a, a+=b); n>>=1); (s*b); }; \\ So we use this one, modified from the one given in A002487
%o A324115 A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
%o A324115 A156552(n) = if(1==n, 0, if(!(n%2), 1+(2*A156552(n/2)), 2*A156552(A064989(n))));
%o A324115 A323244(n) = if(1==n, 0, my(k=A156552(n)); (2*k)-sigma(k));
%o A324115 A324115(n) = A002487(A323244(n));
%Y A324115 Cf. A002487, A033879, A156552, A323244, A323902, A324201, A324116, A324117.
%K A324115 sign
%O A324115 1,8
%A A324115 _Antti Karttunen_, Feb 20 2019